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The closed ideal of (c o ,p,q)-summing operators

Authors:	Aicke Hinrichs Albrecht Pietsch

Institution:	(1) Mathematisches Institut, FSU Jena, D 07740 Jena, Germany

Abstract:	For 1/p+1/q1, we study the closed ideal $\mathfrak{B}_{c_o ,p,q}$ formed by the (c _o,p,q)-summing operators. It turns out thatT:XY does not belong to $\mathfrak{B}_{c_o ,p,q}$ if and only if it factors the mapId:l _p ^l _q. By localization, we get the ideal $\mathfrak{B}_{_{c_o ,p,q} }^{super}$ that consists of those operatorsT for which all ultrapowersT ^u are contained in $\mathfrak{B}_{c_o ,p,q}$ . Operators in the complement of $\mathfrak{B}_{_{c_o ,p,q} }^{super}$ are characterized by the property that they factor the mapsId:l _p ^n l _q ⁿ uniformly. Our main tools are ideal norms.Supported by DFG grant PI 322/1-2

Keywords:	47B10 46B28 46B07
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